In this paper, we consider a two-user multiple access fading channel under quality-of-service (QoS) constraints. We initially formulate the transmission rates for both transmitters, where the transmitters have arbitrarily distributed input signals. We assume that the receiver performs successive decoding with a certain order. Then, we establish the effective capacity region that provides the maximum allowable sustainable arrival rate region at the transmitters' buffers under QoS guarantees. Assuming limited transmission power budgets at the transmitters, we attain the power allocation policies that maximize the effective capacity region. As for the decoding order at the receiver, we characterize the optimal decoding order regions in the plane of channel fading parameters for given power allocation policies. In order to accomplish the aforementioned objectives, we make use of the relationship between the minimum mean square error and the first derivative of the mutual information with respect to the power allocation policies. Through numerical results, we display the impact of input signal distributions on the effective capacity region performance of this two-user multiple access fading channel.